Neil O'Brien is Director of Policy Exchange, an independent think tank working for better public services, a stronger society and a more dynamic economy. He writes in a personal capacity.

So what should the top rate of tax be? It all turns on the long-term effects of high taxes

What effect does a high top rate of tax have on the behaviour of the rich?

Most people want to pay less tax, and there are endless arguments to be had about what's fair. No one agrees about who should pay what, and why. People think different things are fair depending on how people are earning their money (just think about bankers and footballers).

But let's leave aside those arguments about fairness for another time. Let's treat top taxpayers are as if they are just a goose which we want to provide us with golden eggs. If we just want to maximise the long term tax take from top taxpayers, what should we do?

Everyone agrees there's a balancing act. Try and tax people too much (particularly at the top end) and they will either start avoiding the tax, or work less, or retire earlier, or work overseas. Over the longer term, entrepreneurs will be less likely to come in the first place.

That balancing act is formalised in the idea of the Laffer curve. But people disagree about which rate will maximise receipts for the Treasury. In this morning's Guardian, Polly Toynbee argues that receipts only start to fall "when people are taxed at 70 per cent."

What do economists say?

A classic paper by Brewer, Saez and Shephard from 2008 looked at how people had responded to big changes in the top rate in the 1980s. looking at the top 1 of earners, they estimated that the optimal top rate to extract the most tax had been between 64 per cent and 40 per cent depending on the methods used:

Taking values of the elasticity 1 standard deviation either side of the central estimate gives a range for the optimal top rate of 50.4% to 64.5%. But our analysis is also consistent with the current top METR being too high: using the value of the elasticity from the simple difference over the period 1978 – 2003 would give an optimal top rate of 40.2%, and using the difference-in-difference estimate of the elasticity from the same period would imply an optimal top rate of 49.4%.

When the Treasury originally announced the policy it said that in theory it would mean that 300,000 people would pay £7.5bn more – if they didn't change their behaviour.

But of course they would. In fact £4.9bn of that would never materialise because of: people working less, retiring early or leaving the country, more tax planning, avoidance and evasion etc. So they only expected to get something like £2.7bn a year.

However, the new study finds an even bigger underlying behavioural response than the original Treasury calculations did when the tax was introduced. They say the new assumptions are "more in line with the academic evidence than the behavioural estimates used in the March Budget 2010 costing".

The study stresses that the evidence is still very uncertain. But it produces estimates using two different methods showing that the shift from a 40p to 50p top rate either raised a billion a year or lost 1.4 billion a year. (Thanks a bunch economists…)

As a central estimate, they now suggest that in the short term the peak take is somewhere in the high forties (below 50p) As a result they think the cost of moving to 45p is £50-100 million. A lot of money to you or me, but that's equivalent to between 0.005 per cent and 0.01 per cent of total public spending next year. Political dynamite, but a rounding error in public spending terms.

That partly explains, I suppose, the decision to reduce it. Osborne clearly thinks he can easily make up the money from his "mansion purchase tax" and anti-tax avoidance measures.

But there is more to it than that. While the total cost is small, and netted off by other tax rises on the rich, it is still a cost not a benefit. So why do it now?

The HMRC paper makes important distinction between the short and long term effects of high rates of tax.

"The short run and long run behavioural responses to a rate change can also differ. For example, labour supply responses such as migration or changes in employment may take some time"

Quite. Too much of the discussion of the 50p rate has been purely about what if anything it will raise in the short term.

HMRC point out,

"evidence that higher marginal tax rates could affect growth rates in the longer-term, suggesting that the negative impact on GDP could become progressively larger over time."

And note that:

"High marginal rates of income tax risk weighing on the growth potential of the economy by deterring the most highly productive individuals from living and working in the UK, and through deterring the foreign direct investment that can be an important element in the diffusion of new technologies and techniques. These effects are likely to be modest if those who are liable to pay the additional rate of tax expect that it will be temporary.

However, if the rate were to remain at 50 per cent for an extended period, there would be a risk that the effects on growth could become more material. Even a small reduction would erode revenues in the longer run as lower levels or rates of economic growth reduce receipts across the economy. Based on the current tax to GDP ratio of 37 per cent, a £1 billion fall in the level of GDP corresponds to a £370 million fall in tax revenues."

This is the vital thing. UK GDP is currently just over 1,567bn, predicted to rise to 1,652bn next year. Something that increases growth by the slightest, slightest, amount – so that it is, say, 1,653bn, would mean a 370 million increase in tax revenues. That would be four to seven times more than the immediate cost of cutting from 50p to 40p.

This may be the key thing that changed Osborne's mind. If the tiny hit to the public finances is good for growth, then over the long term it mean not slightly smaller tax takes – but radically higher tax revenues.

Could the 50p rate be having a tiny, tiny, negative effect on growth, of the kind that would justify a cut? Actually, it could be having quite a big effect.

If you can attract one Mark Zuckerberg to start the next Facebook here, you could pay for the whole thing. And today, entrepreneurs really do move to lower tax locations. Think about the telecoms company Skype: technology developed entirely in low tax Estonia – by entrepreneurs who had left high tax Denmark and Sweden. In this context it is worth noting that the 50p rate meant we had a higher top rate than any of our G20 competitors:

None of the above will stop people getting very excited about the change from 50p to 45p. Ed Miliband looked really angry in the Commons the other day.

But it is interesting how much of this is about framing. After all, taxes on the rich were lower (40p) for almost all of his time in Government. Labour had 13 years in office, but the 50p rate came in just 36 days before they left Downing Street.

That means, if my calculations are right, that 99.25% of their time in office was covered by disgraceful, lickspitle, capitalistic Blairism (a.k.a the 40p rate) and just 0.75% of the time by the heroic pip-squeakin', tax raisin' socialism (i.e. the 50p rate).

You could say that, ah well, now it is inappropriate for the rich to pay less because of the recession. That makes political sense, but not policy sense.

After all, there were people in poverty all the way through the boom too. If the 50p rate is a good idea now, why wasn't it a good idea then? Unless there is an economic argument that the higher rate will raise more – once long term effects are taken into account – then the case for it is purely political.

So was it the right thing to do? I think the politics of it will be really tough for the government, but it was the right thing to do economically.

Interestingly, Ed Miliband is not promising to reintroduce the 50p rate. So that's one vote of confidence at least.